Short answer: ask it a set of questions your pages should be the natural source for, and look at whether your domain appears in the sources attached to the answer. A negative result means one of three things, and they need different fixes.

Do the check properly

Three rules or the result is meaningless. Use questions that do not contain your brand name — a named question retrieves your site trivially and proves nothing. Run each question more than once, because answers vary between runs. And only count your domain if it appears as a source marked in the answer, not merely because the answer happens to describe you.

Reading a negative result

What you seeLikely causeWhere to look
Never cited, competitors citedAccess or extractionFetch your page as each named agent; then read the first two sentences under a heading out of context
Cited but not recommendedCorroborationThird-party mentions, directory listings, comparison pages you don't own
Sometimes cited, inconsistentlyNormal varianceNothing — this is the expected pattern; measure a rate over many questions instead of judging single runs

The mistake we made ourselves

Early on our own product judged "cited" from a 500-character excerpt of the answer text — an excerpt that never included the source URLs. So a question could be listed as cited on one screen and "not mentioned" on the next. The fix was to derive the flag from the actual citation URLs and match on our own domain. If you are building this check yourself, look at where your "cited" boolean comes from before you trust it.

The other direction

A citation is not a recommendation. Being used as reference material while the answer suggests a competitor is a specific, common and fixable outcome — but you will never see it if you track one combined number.